Bathymetry, heat output and convection in Ruapehu Crater Lake, New Zealand

Journal of Volcanology and Geothermal Research, 9(1981) 215--236

215

Elsevier Scientific Publishing Company, Amsterdam -- Printed in Belgium

BATHYMETRY, HEAT OUTPUT AND CONVECTION IN RUAPEHU CRATER LAKE, NEW ZEALAND

A.W. HURST and R.R. DIBBLE

Geophysics Division, Department of Scientific and Industrial Research, P.O. Box 1320, Wellington (New Zealand) Geology Department, Victoria University of Wellington, Private Bag, Wellington (New Zealand) (Received August 21, 1979; revised and accepted July 11, 1980)

ABSTRACT Hurst, A.W. and Dibble, R.R., 1981. Bathymetry, heat output and convection in Ruapehu Crater Lake, New Zealand. J. Volcanol. Geotherm. Res., 9: 215--236. Bathymetric observations of Ruapehu Crater Lake show that it became shallower and its volume decreased by 3 × 10' m 3 between 1965 and 1970. It is likely that this was due to lava moving upwards in the region under the lake. From the regular measurements of Crater Lake temperature, outflow, and chloride and magnesium ion concentrations, the inflows of steam, cold water and chloride and magnesium ions were calculated, using the 1970 volume. Only about half the precipitation falling on and around the lake mixes with the lake water, since the cold fresh water floats on top of the denser lake water, and travels to the outlet without mixing with the main body of water in the lake. The chloride content of the input steam appears to vary with time, in a similar fashion to that of White Island fumaroles. Temperature and density profiles of the lake in 19'65 and 1966 indicated that convection was occurring. The temperature profile of the top 175 m of the lake agreed with a model of turbulent convection in small cells, giving a temperature gradient at any level in the lake proportional l~o the heat flux at that level. The convection model predicted that the temperature at depth would exceed the local boiling point if the thermal power input reached a value which wc~dld sustain a surface temperature approaching 60°C. This prediction of instability was not inconsistent with observations. Convection in the present Crater Lake probably occurs in the form of thermal plumes from small sources.

INTRODUCTION

Ruapehu is an active andesite strato volcano, 2797 m in height, located near the centre of North Island, New Zealand (lat. 39°17'S, long. 175°31'E, Catalogue of Active Volcanoes No. 4, 1--10) (Cole and Nairn, 1975). Its active south crater is occupied by Crater Lake, which has an area of 0.2 km 2, and "acts as a steam condenser, and hides as it were to some extent the activity of R u a p e h u " (Friedlander, 1898). It also acts as a calorimeter, chemical 0377-0273/81/0000--0000/$02.50 © 1981 Elsevier Scientific Publishing Company

216

collecting apparatus, and measuring platform, and allows the integrated volcanic activity to be easily measured (Dibble, 1974). Flows of water and mud from Crater Lake have produced numerous lahars (Gregg, 1960), including one on 24 December 1953 which swept away the Tangiwai railway bridge as an express train was approaching, causing the loss of 151 lives (O'Shea, 1954). Important eruptions have occurred in 1861 and 1945 (Gregg, 1960), in 1969 (Dibble, 1974; Healy et al., 1978), and in 1975 (Nairn et al., 1979). Bathymetric surveys of Crater Lake were made in 1965 (Dibble, 1972, 1974) and 1970 (Irwin, 1972). The results of these surveys, plus some other depth measurements, show that the lake's depth and volume have changed considerably in the last twenty years. Occasional inspections of Crater Lake have been made, usually by N.Z. Geological Survey staff, since 1946. More regular inspections at approximately monthly intervals, with measurements of lake temperature, outflow pH, and some chemical concentrations, date from 1966. The results of these inspections are published in N.Z. Volcanological Record (Healy, 1973a, b; Nairn, 1974, 1975a, b, 1976; Scott, 1977, 1978), and were used to calculate a heat and mass balance for Crater Lake. The analyses of chloride and magnesium are from Giggenbach (1975) and Giggenbach and Glover (1975), with some extra values (W.F. Giggenbach, personal communication, 1978). The temperature and density soundings made by Dibble (1972, 1974) in 1965 and 1966 are used to re-examine the convection mechanism in the lake, and to consider the stability of the temperature profile in Crater Lake. BATHYMETRY

The earliest evidence of changes in the depth of Ruapehu Crater Lake relative to normal overflow level was the appearance in March 1945 of an island of molten lava (a "tholoid") just southeast of the centre of the lake (Reed, 1945; Cotton, 1946; Odell, 1955). This grew to entirely replace the lake in July 1945 (Beck, 1950), and was then progressively destroyed by explosion and collapse to leave a pit about 300 m deep by January 1946 (Odell, 1955; Gregg, 1960). This pit then gradually filled with water. In 1950, the greatest depth of the reformed lake found by members of the N.Z. Canoeing Association was 70 m, while most of the lake was 18--40 m deep, but its level relative to overflow level was not observed. By December 1953, the lake had risen to 7.6 m above normal overflow level (Rose, 1954) due to a dam of ash and lava blocks which formed during the 1945 eruption. After the dam failed and the lake drained rapidly to overflow level to cause the Tangiwai disaster on 24 December 1953, further canoeists recorded approximately the same depths in 1954 as in 1950. In 1965, Dibble (1972, 1974) made soundings with a Kelvin sounding winch and a metering pulley at 26 stations located within 8 m by compass bearings to marker poles and mountain peaks. The lake volume was 9.4 X 104 m 3, the average depth was 47 m, and the maximum sounding was

217

298 m. About 12% of the lake area was 100 m deep or more. Probably the canoeists had missed this deeper area, because the maximum depths in 1946 and 1965 were similar, and the mild volcanic activity between 1946 and 1965 reported by Gregg (1960) and Dibble (1974) was unlikely to have caused the apparent variations in depth.

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218

In January 1970, the lake was resurveyed with an echo sounder by Irwin (1972) during a co-operative expedition involving the N.Z. Department of Scientific and Industrial Research (D.S.I.R.), Victoria University of Wellington, and the N.Z. Defence Department, and found to have volume 6.2 × 10 ~ m ~, average depth 28 m, and a greatest recorded depth of 80 m (Fig. 1), obtained by line soundings in the area of previous greatest depth. Not only had the lake decreased considerably in volume during the volcanic eruptions of 1966 (Clacy, 1972; Dibble, 1972, 1974), 1968 (Dibble, 1969, 1974), and 1969 (Dibble, 1974; Healy et al., 1978), but its shape of cross section had changed from a champagne glass to a bowl (Fig. 2). Only once, during the day after the 1966 eruption, was the lake observed to be overflowing and agitated as one would expect if lava was flowing in at the bottom (Dibble, 1974). S

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Trending NNW-SSE across the northern half of the lake (Fig. 1) there was an elongated area where echo-sounder reflections were scattered back from rising bubbles in the lake water (Fig. 3). Presumably this was an area of submerged hot springs and fumaroles in the lake floor. Where the scattering completely obscured the bottom reflections, large vents in the floor could exist.

Fig. 3. Echo-sounder records along two tracks in 1970, showing effect o f rising gas bubbles. See Fig. 1 for tracks,

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HEAT AND MASS BALANCE OF CRATER LAKE Method Crater Lake temperatures and outflows (or levels if lake is below overflow level) are measured a b o u t once a m o n t h b y D.S.I.R. staff from Wairakei and Rotorua. Water samples are collected on these trips, and the samples are analysed for chloride and magnesium ion concentration at Chemistry Division, D.S.I.R. From these measurements it is possible to calculate heat and mass flows into and out of Crater Lake. Previous w o r k along these lines has been done b y Dibble (1965, 1966, 1974), Giggenbach (1974), and Giggenbach and Glover (1975). The t w o latter papers used chloride ion concentration as an indicator of fumarolic steam input, and magnesium ion as an indicator of interaction of water and hot rock. These t w o ions were selected because they are n o t contained in any mineral precipitated from Crater Lake, so their concentrations are n o t affected b y solubility considerations. The magnesium content of the lake increase during eruptions and for up to t w o months afterwards as the lake water interacts with hot andesitic material. (Giggenbach and Glover, 1975). The rest of the time it would be constant were it n o t for the magnesium which leaves in the outflow from the lake. An initial estimate of the energy entering Crater Lake is made by summing the energy lost at the lake surface and the change in heat energy stored in the lake. The surface energy loss is calculated from the formula given in the Appendix, making the assumption that the lake temperature changes linearly between measurements. Provided that the shape of the vertical temperature profile does not change drastically, the change in stored energy is the change in surface temperature multiplied by the thermal capacity of the lake. The area and volume of the lake are taken as 200,000 m 2 and 6,000,000 m 3, respectively, when it is full (see preceding section). If it is below the overflow level, the area and volume are calculated from formulae based on the b a t h y m e t r y of the previous section. The steam input required to be condensed in the lake to give this energy input is then calculated, using an assumed enthalpy relative to water at 0°C of 3.0 MJ/kg. A thermal p o w e r of 100 MW corresponds to a b o u t 36 l/s of steam. It is assumed that all heat lost b y the steam after it passed the old lake b o t t o m at 300 m depth is gained by the lake. At 300 m depth, the pressure is 30 bar, giving a steam saturation temperature of 235°C. It is likely that the steam would be slightly superheated, so 260°C is taken as the steam temperature, giving an enthalpy of 2.89 MJ/kg. The steam probably contains 5--10% of other gases, particularly carbon dioxide (based on White Island fumaroles analysed b y Giggenbach, 1975), and this makes a contribution of a b o u t 0.06 MJ/kg to the enthalpy, calculated per mass of condensed steam. A very arbitrary 0.05 MJ/kg allows for the heating effect of any steam which is n o t condensed on its way through the lake.

221 If the lake is below overflow level, the volume change of the lake between measurements is calculated from the measured level change. If the lake is overflowing, however, the total outflow between measurements is calculated from the decrease in magnesium concentration due to dilution. For example, if the magnesium concentration has decreased by 5% between t w o measurements, then the total outflow between those measurements was approximately 5% of the lake volume. During and immediately after eruptions, magnesium is being added to the lake, and the outflow has to be estimated, using measured outflows. The measured outflows, being spot measurements of a quantity which is considerably affected b y time of day and weather, do not give a good estimate of the average flow over a period. The use of magnesium concentration to calculate dilution factors assumes that the chemical concentrations are uniform throughout the lake (as was observed by Dibble, 1974). In this study, it was found that a few measurements gave anomalously low chloride and magnesium concentrations, and low temperatures. These measurements suggested that cool fresh water, which had a lower density than the bulk of the lake water, was concentrated in a surface layer. Rishworth and Lloyd observed on 23 December 1969, that melt water did not mix with the rest of the lake, but travelled across the surface to the outlet as a separate layer (E.F. Lloyd, personal communication, 1969). However, providing water samples are taken in the lake itself, at a depth of 0.2 m or more, rather than the outlet stream, there is no reason to d o u b t that they will be representative of the lake as a whole. The total quantity of chloride added to the lake is calculated from the measured concentrations, with adjustment for lake volume and the effect of the outflow. The magnesium input to the lake during and after eruptions can also be calculated, b u t all calculations for these periods are only estimates, as accurate outflows are not known, since they cannot be calculated from the magnesium dilution. The chloride and magnesium inputs during eruptions are probably underestimated, as estimates of the outflow generally do not allow for the extra o u t f l o w produced by water surges from eruptions. The cold inflow of melt water into the lake is calculated from the equation: cold inflow + steam input = evaporated water + (volume change) (or outflow ) All quantities are mass changes between measurements The total evaporation is calculated from the evaporation rate formula in the Appendix. The cold water coming in requires a certain amount of heat to bring it to lake temperature, and the cold inflow and steam input are adjusted to allow for this.

222

Results The heat input to the lake is shown in Fig. 4, for the period 15 February 1966 to 31 December 1978. The graph is of thermal power, which is roughly proportional to the rate of steam input. The power is always positive, although on some occasions it is very small, as if the steam conduits under the lake were blocked. This seems to be reasonable, and suggests in particular t h a t the evaporation heat loss formula is approximately correct. "{Dibble {1972) and Giggenbach and Glover {1975) used evaporation heat loss formulas giving 50--100% higher losses). The power input to Crater Lake is usually between 100 and 700 MW. Fig. 4 also shows cold inflow, which was smoothed over approximately 60-day intervals. Generally cold inflow is high during the Summer and Autumn, and close to zero for Winter and Spring. The cold inflow should never be negative, so the negative values are probably because of errors in level readings or because the water samples analysed were not representative of the lake as a whole. To check the internal consistency of the measurements, the calculated total cold inflow was summed for the nine winter to winter years in which there were no disturbing eruptions. The mean annual value was 1.10 × 106 m 3, with a standard deviation of 0.38 × 104 m 3. The average annual rainfall at the nearest weather station (The Chateau) is approximately 3.0 m, the lake has an area of 200,000 m 2 and a catchment of approximately 500,000 m 2 of snowfields. If all the precipitation eventually enters the lake as melt water, the average annual cold inflow should be about 2.1 × 106 m 3 instead of 1.1 × 10 6 m 3. An adequate explanation for this discrepancy is that fresh water entering the lake can float on top of the denser lake water, and it will flow out of the outlet w i t h o u t fully mixing with lake water. This behaviour has already been mentioned, as an explanation of anomalously low temperatures and chemical concentrations. Since the outflows were calculated from dilution of chemical constituents, water which passes across the lake surface w i t h o u t mixing is not included in either inflow or outflow values. In other words, only about half of the cold water entering the lake is mixing with the lake water. The snowfield around the lake is probably accumulating snow between eruptions, and this also tends to explain the discrepancy. {Since 1953 when there was flat ground on the north shore of the lake, snow has accumulated to form ice cliffs about 30 m high.) Chloride and magnesium inputs to the lake are shown in Fig. 4. Fig. 4 also shows chloride percentages in the steam, averaged over long periods. This was done to smooth short-term variations in apparent chloride input. The greatest chloride concentration was 1.09%, after the 1968 eruption, and the values were general)y about 0.7--1.0% during and after eruptions. (Giggenbach and Glover (1975) gave a higher value of 1.2% for 1971--1972 because they used a greater lake volume in their calculations.)

223 Long periods of lower chloride concentration correspond to the periods in which Giggenbach and Glover {1975) assumed that the steam vents were blocked, and pressure was building up, leading to an eruption. It appears that the low chloride addition in fact indicates a change in the chemical composition of the volcanic gases. This would be similar to the White Island fumaroles described b y Giggenbach (1975), as the chloride contents of these fumaroles tended t o decrease with time after the 1971 eruption of White Island. The continuing p o w e r input to Crater Lake indicates that steam vents are not blocked for long periods. It will be n o t e d that the 1966, 1968 and 1971 eruptions of Ruapehu were preceded b y and associated with fumarotic heating of the lake, and considerable addition of heat and chloride continued for months after the eruption. The 1969 and 1975 eruptions were essentially single brief events and had little effect on the chloride content of the lake. Between February 1966 and December 1978, a b o u t 37 million tonnes of condensed fumarolic steam, and 175,000 tonnes of chloride were added to the lake. This did not include any material erupted through Crater Lake, unless it immediately returned to the lake. The quantity of magnesium added between 1966 and 1970 was roughly 8000 tonnes. Using the Giggenbach and Glover (1975) figures of 2.78% magnesium in andesitic lava, this corresponded to the disintegration of a b o u t 300,000 tonnes of lava. This could perhaps have produced about 300,000 m 3 of watery sediment at the b o t t o m of the lake, which only explained 10% of the observed lake volume change, of 3 × 104 m 3, between 1966 and 1970. This discrepancy, and the fact that the addition of another 14,000 tonnes of magnesium after 1970 did not apparently result in any great decrease in lake volume of the lake (no proper survey has been made, but the behaviour of telemetry b u o y s on ropes of known length gives some idea as to the depth), suggest strongly that some mechanism other than the addition of hydrothermally altered andesite has decreased the volume of the lake. The likely cause is that lava came up into the b o t t o m of the lake at some time, but was protected b y sediment and cooled blocks of lava from contact with the lake water, so that it cooled slowly and did not release much magnesium into the lake. This probably occurred during the 1966 and/or 1968 eruption. This is consistent with analysis of the ejecta from the 1969 Ruapehu eruption, which showed that the ejecta contained substantially unaltered pumice lapilli, apparently formed in the 1966 eruption (Healy et al., 1978, p. 59).

CONVECTION IN THE CRATER LAKE As the average heat flux in Crater Lake is in the range 500--3500 W/m 2 (for surface heat losses of 100--700 MW), which is at least a thousand times greater than could be sustained by conduction alone, convection must norreally be occurring.

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A quantitative analysis of this convection requires information on the variation of temperature with depth in the lake. Useful deep temperature and density measurements (Fig. 5) were made in 1965 and 1966 {Dibble, 1974), b u t have not been repeated. Therefore the results of this section apply to Crater Lake as it was then (see section " B a t h y m e t r y " ) , i.e. with a maximum depth of a b o u t 300 m.

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Free thermal convection occurs when the b o t t o m layers of a homogeneous fluid are heated sufficiently. They expand, become lighter than the t o p layers, and rise, carrying heat with them. For convection to occur, the Rayleigh number must exceed a critical value. The complex shape of Crater Lake makes accurate calculation of the Rayleigh number very difficult, but semi-quantitative calculations can readily be made. If the top 100 m of the lake is considered to be a region of large horizontal extent with a fixed temperature differential of 8°C between the surface and 100 m depth {from Fig. 5), then the Rayleigh number can be calculated from:

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227

This gives a value of 2.5 × 1017 for Ra. The critical value of Ra is of the order of 1000 (Turner, 1973), so extremely vigorous convection was occurring. It can be seen from the above values that only an infinitesimal temperature gradient was required to make the top part of the Crater Lake convect. However, as will be shown later in this section, the actual value of the Rayleigh number was also important as it determined h o w much heat was transferred by convection. The above calculations do not take account of the effect of suspended sediment on density. Measurements b y R.R. Dibble in 1966 showed that the relative density of Crater Lake water samples when measured in the laboratory increased by 0.0068 between surface samples and a sample from 200 m depth (Fig. 5). This increase was almost entirely due to the presence of increasing quantities of fine sediment, as the concentration of dissolved compounds did not vary appreciably with depth. However, when the measured densities were corrected for temperature, the actual lake density (relative to water at 15°C) decreased from 1.0165 at the surface to 0.998 at 200 m. There is a possible error in these measurements, in that during the recovery of the water samples, particles of sediment greater than 0.1 mm in diameter could have been lost from the sampling tube when it was being hauled to the surface. Although all sediment collected in surface samples was very fine, if larger particles of sediment were present at depth, their loss could result in a slight underestimate of the density at depth. The general decrease in density with depth shown in Fig. 5, is consistent with a convection regime which explains the high heat flow through Crater Lake. A review of double-diffusive convection, in which two variables, in this case temperature and sediment concentration, affect b u o y a n c y is in chapter 8 of Turner (1973). Baines and Gill (1969) showed that for the Crater Lake situation, in which the temperature increased downwards, convection will occur in the presence of a stabilising density gradient (due to sediment) as long as the Rayleigh number calculated from the overall density gradient was larger than a critical value. (This of course required an overall unstable density gradient, otherwise Ra would be negative). This corrected an earlier result by Veronis (1965), on the basis of which Dibble (1974) concluded that convection was n o t occurring in Crater Lake. The measurements made b y Dibble in 1965 and 1966 showed that the stabilizing density gradient due to sediment was a b o u t 30% of the unstable density gradient due to temperature. This reduced the Rayleigh number by 30%, which does n o t have great significance at the very high Rayleigh numbers in Crater Lake. The narrow throat of Crater Lake, which was at least 300 m deep in 1965, approximated a long vertical pipe. Hales (1937) analysed convection in such a pipe using a Rayleigh number calculated by: g~ dT 4

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where r = Radius of pipe. The critical value of R a was found to be a b o u t 200. Using this formula, with r = 60 m (approximate value at 150 m depth): d T / d z = 0 . 7 ° C / m ( a p p r o x i m a t e value at 1 5 0 m d e p t h ) a = 5.8 × 10 -4 m2/s f o r w a t e r at 70°C v = 4.1 × 10 -~ m2/s for w a t e r at 70°C

gives R a = 8 × 1017, in order of magnitude agreement with the calculation for the t o p part of the lake. The convective heat flux through the lake depended on the Nusselt number, defined as: total heat flux Nusselt number, N u = (3) conductive heat flux Turner (1973, chapter 7) discussed N u , and concluded that for high Rayleigh number, the applicable formula is: N u = k R a ys

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(where A -- cross-sectional area; and K = thermal conductivity, 0.6 W/m °C for water) from (3) and elementary heat conductive conduction theory. For the t o p 100 m of Crater Lake, for which R a was 2.5 × 1017, N u would have been a b o u t 65,000 b y equation (4), which would have given a total heat flux of a b o u t 500 MW, compared to the actual heat loss of 210 MW for a surface temperature of 32°C. All the above calculations are only order of magnitude estimates, as there is no justification for arbitrarily dividing the Crater Lake into regions, and calculating a Rayleigh n u m b e r for each region. What the calculations do suggest is that convection was responsible for the observed heat flux. In very turbulent convection (say, R a > 109), the convection pattern is dominated b y small-scale turbulent motions in the fluid (J.L. Robinson and R.A. Wooding, personal communication, 1979). This would have been expected to apply to Crater Lake, where R a was of the order of 1017. With small-scale motions dominant, the side boundaries would n o t have much influence on convection in most o f the lake, so a first approximation would be that the convection pattern was similar throughout the lake, with Ra, and hence N u constant. If the lake was in thermal equilibrium, then the heat flux through each horizontal cross-section was the same. Then by (5), the local temperature gradient must be inversely proportional to the cross-sectional area.

229 The bathymetric contours shown in fig. 26 of Dibble (1974) were used to calculate the cross-sectional area as a function of depth in Crater Lake as it was in September 1965. From a smooth curve of horizontal cross-section versus depth, inverse area (proportional to temperature gradient) was calculated at 10-m intervals, and integrated to give the shape of the theoretical temperature versus depth curve. By adjusting the additive and multiplicative constants relating the temperature to the integrated inverse area, the theoretical curve shown in Fig. 5 was obtained. There is reasonable agreement between this theoretical curve and the temperatures measured in 1966 from the surface to a depth of 175 m. Below this, the actual measured values showed a kink which is n o t explained b y any convection model. Possibly, heat was entering the side of the lake at depths below 175 m, rather than coming from greater depths. Alternatively, the heat m a y have been carried b y steam bubbles, which did not give up all their heat to the lake water until t h e y had risen some distance from the deepest part of the lake. The theoretical curve shown in Fig. 5 corresponded to a product of crosssectional area and temperature gradient of: 8140 m 2 × (°C/m) Substituting this in equation (5), and using a total heat flux of 220 MW, derived b y the formula in the Appendix for the total surface heat loss at a lake surface temperature of 31.5°C gave a Nusselt number of 45,000. By equation (4), this corresponded to a Rayleigh n u m b e r of 9 X 1016. The Rayleigh n u m b e r for convection in the lake as a whole would be expected to be larger than either of the numbers calculated earlier for parts of the lake (3 X 1017 for the t o p 100 m, and 8 X 1017 for a portion of the throat), b u t the effect of sediment would lower the effective Rayleigh number. The Rayleigh number calculated from the lake dimensions and that calculated from the heat flux, are therefore within one or t w o orders of magnitude, which is about as much agreement as one would expect from a simple model. The detailed temperature profile obtained from a bathythermograph in September 1965 (Dibble, 1974) is shown in Fig. 6. It shows considerable fluctuations of temperature with depth, including decreases of temperature with increasing depth. There also appear to be regions in which the temperature is approximately constant for 10 m or so. Turner (1973) describes h o w in high Rayleigh n u m b e r convection, the temperature in most of the convecting region is approximately constant, with rapid temperature changes at the boundaries of the convecting region. The bathythermograph record suggests that Crater Lake was made up of convecting cells, of typical vertical extent of 10 m, each of approximately uniform temperature, b u t with high temperature gradients on their interfaces with other cells above and below. The cells were probably only transitory, especially since the ascending and descending bathythermograph profiles differed markedly. (These differences

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. . . . . . T E M P E R A T U R E , °C

-,5

Fig. 6. Bathythermogram taken just south of the centre of Crater Lake in September 1 9 6 5 . T h e pressure t r a n s d u c e r was r e a d i n g a b o u t 10 m t o o s h a l l o w when ascending ( t o p

trace).

could also have been due to horizontal temperature gradients, if the b o a t drifted during the sounding.) These cells are probably a feature of the double-diffusive convection, with step changes of temperature and sediment content compensating to give the same density on each side of the cell boundary. This would be similar to the layering phenomena c o m m o n l y observed in less turbulent double-diffusive convection (Turner, 1973). No temperature soundings have been done since Crater Lake became much shallower, so nothing can be said a b o u t its present state, other than that it is still convecting. The concentration of upwelling observed in certain parts of the lake, and the presence in certain areas of rising gas bubbles (see Figs. 1 and 3), suggest that the present convection pattern is that of one or more plumes of hot water, each rising from a comparatively small source. The temperature pattern produced by convective plumes in a confined space was derived b y Baines and Turner (1969). They showed that the hot water upwelling from a heat source would entrain cold water as it rises to the surface, where the n o w warm water spreads out before descending. This means that when a source of heat starts to produce a convective plume, the t o p layer of the lake is heated comparatively quickly, before lower layers have been significantly affected. An attempt was made to use the plume model for Crater Lake in its 1965--1966 state (300 m deep) b u t it did not fit the observed temperature profile. There are two reasons w h y the plume model was inappropriate.

231

Firstly, Crater Lake's depth was then greater than its radius, a case for which Baines and Turner (1969) said a general overturning of the lake was likely to occurrrather than the stable plume pattern. Secondly, in the deep constricted part of the lake, the basic plume assumption, that cold water can be entrained into the ascending plume, is probably not satisfied. STABILITY AND O V E R T U R N I N G OF C R A T E R LAKE

There are several possible instabilities of a vigorously convecting lake such as Crater Lake. The most obvious is disruption of the whole Crater Lake b y major volcanic activity. One of the aims of studies of Crater Lake is to try and identify precursors of such activity. A major problem with this has been that possible precursors of major volcanic activity, such as increases in Crater Lake temperature, could be confused with the effects of convective instabilities in Crater Lake. At present there is no single feature which could be regarded as a precursor of volcanic activity, b u t work is continuing. One instability which can produce a minor eruption in the lake itself is explosive boiling at depth. If the temperature at a certain depth exceeds the boiling point of water under the pressure at that depth, the water can boil producing a bubble of steam. Under favourable conditions, this steam bubble will rise towards the surface, expanding as it goes. The arrival of the bubble at the surface will result in a small hydrothermal eruption at the lake surface. Eruptions of this type are often observed when the lake temperature is above 40°C. Consider the situation at a depth of 175 m. This depth is selected because it is the greatest depth for which the simple convection formula appeared to be valid. The total pressure is 1.79 MPa (17.9 bar) for which pressure the boiling point of water is 207°C. If Crater Lake is in equilibrium with a lake surface temperature of 52°C, the thermal p o w e r loss at the surface equals the power input and has a value of 600 MW. The temperature gradient within the lake for this power throughout is such that the temperature at 175 m will be a b o u t 207°C, i.e. the lake will be on the margin of a boiling instability. The temperatures measured on several occasions in the two weeks following the 24 July 1966 eruption were all a b o u t 53--54°C, which may mean that this was the highest possible stable surface temperature for Crater Lake as it was then. The highest temperature recorded in Crater Lake is 60°C, but this was first recorded in 1968, by which time the lake was probably shallower than 175 m. As it was in 1970, with a maximum depth of 80 m, Crater Lake would be t o o shallow for boiling in the lake to be likely. If the lake is still this shallow, sudden increases in temperature are likely to be caused by new heat sources starting convective plumes. As was already mentioned, Baines and Turner (1969) found that if depth was less than the surface radius, the heating effect of a plume would first be felt at the surface, and then steadily move

232 downwards. This would explain the sudden temperature rises recorded by a temperature measuring buoy which transmits a temperature every few minutes (Hurst, 1980). An example of this was a rise of 6°C in about 16 hours on 12--13 June 1978. If such a temperature rise had occurred evenly through the lake, it would have required an improbably high power input to the lake. This temperature rise was not preceded by earthquakes immediately under Crater Lake. Some other temperature increases immediately followed such earthquakes, and were practically certainly the result of otherwise unobserved small eruptions (Hurst, 1980). CONCLUSIONS Between the bathymetric survey in 1965 and that in 1970, the volume of Crater Lake decreased by about 3 × 106 m 3, with the deeper part of the lake becoming filled up with solid material. The amount of magnesium released into Crater Lake corresponded to the interaction of lake water with only about 300,000 m 3 of andesitic lava. This suggests that the hot andesitic lava, which is assumed to be underneath Crater Lake, pushed colder lava, country rock and sediment into the lake, with only a small fraction of the lava interacting with the lake while it was still hot. The time when this most probably occurred was during and after the 1966 and 1968 eruptions (Dibble, 1974), in which high lake temperatures persisted for several weeks. The heat balance calculations of Crater Lake show that, except for very short periods, there is a significant steam input into Crater Lake. The chloride content of the steam is variable, being generally highest during periods of sustained fumerolic activity, and then falling away almost to zero after six to twelve months. This is fairly similar to the behaviour of White Island fumeroles, which Giggenbach (1975) considered were fed from three different gas sources of differing chemical compositions. Only about half of the cold water entering Crater Lake effectively mixes with the lake water. This is because the comparatively fresh cold water is lighter than the salt and sediment-laden lake water, and floats on top of the lake on its passage to the outlet. When the Crater Lake was 300 m deep, in 1965, the temperature profile fitted a small-scale turbulence model well down to 175 m. The change in the temperature profile below 175 m indicated that either heat was entering the lake at this level, or heat was being carried through the bottom part of the lake by steam rather than water. In the present shallower lake, the heat is probably carried by thermal plumes originating from certain points in the bottom of the lake. The presence of these plumes would explain why the lake surface temperature sometimes increased by several degrees Celsius in a fairly short time.

233 Such rises in temperature increase the problems in using lake temperature as a possible precursor of eruptions of Ruapehu. It is possible that lake temperature, when combined with seismic information, might show whether changes in the temperature reflect deeper changes in the mountain, and hence give the possibility of warning of at least some eruptions, and this possibility is being explored. ACKNOWLEDGEMENTS

We would like to express our appreciation of the efforts made by a large n u m b e r o f people, especially D.S.I.R. staff at Wairakei and Rotorua, in obtaining the Crater Lake temperatures and samples used in this work. We would also like to thank Dr. W.F. Giggenbach, Chemistry Division, D.S.I.R., for unpublished analyses and helpful discussions, and Drs. R.A. Wooding and J.L. Robinson of Applied Mathematics Division, D.S.I.R., Dr. H.E. Huppert, Department o f Applied Mathematics and Theoretical physics, Cambridge, and Dr. T.G.L. Shirtcliffe, Physics Department, Victoria University of Wellington.for discussions on convection. Drs. W.I. Reilly and T. Hatherton of Geophysics Division, D.S.I.R., and Prof. F.F. Evison of the Institute of Geophysics, Victoria University of Wellington have critically read the manuscript and made helpful suggestions. APPENDIX -- SURFACE HEAT LOSS FROM CRATER LAKE The values used here for Crater Lake heat loss b y evaporation and convection into the atmosphere are based on the results of Weisman and Brutsaert (1973). Their theoretical model included t w o factors which are of importance in the convection situation considered. Firstly, the lake temperature is well above ambient, so the lake tends to produce free atmospheric convection, to supplement the forced convection which occurs when winds blow. Secondly, the large area of the lake means that air passing over it becomes more saturated with water vapour, and so less effective for evaporation. In their numerical analysis, Weisman and Brutsaert (1973) expressed the heat loss from the lake as the sum of t w o similar terms. evaporative heat loss = L A E (qw - qa)U W convective heat loss where A P L

= = = Cp = qw =

= p C p A E (Tw - Ta)u W

cross-sectional area of lake (200,000 m 2) air density (0.948 kg/m 3) latent heat of vaporisation of water (2.4 MJ/kg) specific heat of air at constant pressure (1005 J/kg K) saturation vapour concentration of water in air at lake temperature (0.064 kg/m 3)

234

qa

= actual vapour concentration of water in air upwind of lake (0.0022 kg/m 3) Tw = lake temperature (40°C) T a = ambient air temperature (0.9°C) u = friction velocity, m/s (see text) v = wind velocity at anemometer height E is the non-dimensional average vapour or heat flux, averaged across the lake. The same value applies for vapour and heat because the two fluxes are the result of the same turbulent mixing process. The wind speed (v) at a height x above the l~ike.is normally fitted to a logarithmic velocity profile, using the formula (Sutton, 1951): U

x

v=-ln K

Z

(K is the Von Karman constant, usually taken as 0.35)

Z is called the roughness length, and Weisman and Brutsaert (1973) found 2 × 10 -4 m a suitable tvalue. It is the distance above the lake at which the logarithmic profile predicts a zero velocity. This value of Z gives u = v / 3 0 , where v is the wind velocity at anemometer height (6m). E was calculated by Weisman and Brutsaert (1973) by using a numerical m e t h o d for solving the turbulent diffusion equations relating to the upwards movement of water vapour and heat from a water surface. They found t h a t for a warm lake, E increased considerably for small values of v. This is because, for small wind velocities, free convection in the air above the lake added significantly to the heat and mass flux. As the width of the lake increased, E decreased, because the air became more humid and warmer as it crossed the lake, so for a large lake the air was less efficient in picking up heat and moisture. The width of Crater Lake was taken as 500 m. For Crater Lake at 40°C, the values shown above in brackets apply (meteorological parameters are as used by Dibble, 1972). By interpolating in the results of Weisman and Brutsaert (1973), E is found to be 0.04 for v of 10 m/s, increasing to 0.075 at 2 m/s. This results in heat losses by evaporation and convection of 180 MW at 2 m/s and 470 MW at 10 m/s. Dibble (1972) obtained 437 MW at zero wind velocity and 580 MW at 10 m/s, using an eml~irical relationship. The only information on wind velocities are Meteorological Office estimates that in free air at that altitude, the mean annual wind velocity is about 12 m/s. Because of the sheltered position of the Crater Lake, 5 m/s has been assumed. The total lake power loss also includes a radiative component. The radiative power loss is: (T¢

-

T:).4 W

where a = emissivity (0.8 for rough water surface) and C = Stefan's constant (5.67 × 10 -8 W/m ~ K4). At Tw = 40°C, Ta = 0.9°C, this is 43 MW.

235

The total lake power loss, and the evaporation rate (used for water balance calculations) were calculated at 5°C intervals from 20 to 60°C using 5 m/s average wind velocity (E = 0.05). The two polynomials listed below fitted the calculated values within 1%, and were used in the calculations of power and water balance: total power loss (MW) = 0.005630 T 3 - 0.3012 T 2 + 13.55 T - 81.3 (for 200,000 m ~ lake surface) evaporation r ~ e ( m / d a y ) = 9.49 × 10-7T 3 - 0 . 0 0 0 0 4 7 6 T : + 0.00169 T - 0.0104

where T = lake temperature (oC).

REFERENCES Baines, P.G. and Gill,A.E., 1969. O n thermohaline convection with linear gradients. J. Fluid Mech., 37 : 289--306. Baines, W.D. and Turner, J.S., 1969. Turbulent buoyant convection from a source in a confined region. J. Fluid Mech., 37: 51--80. Beck, A.C., 1950. Volcanic activityat Mt Ruapehu from August to December 1945. N.Z. J. Sci. Technol., B31: 1--13. Clacy, G.T., 1972. Analysis of seismic events recorded with a slow motion tape recorder near Chateau Tongariro, N e w Zealand, during February 18, 1966 to December 31, 1966. Bull. Volcanol., 36: 20--28. Cole, J.W. and Nairn, I.A., 1975. Catalogue of the Active Volcanoes of the World Including Solfatara Fields, XXII. N e w Zealand. IAVCEI, Rome, 156 pp. Cotton, C.A., 1946. The 1945 eruption of Ruapehu. Geogr. J., 107: 140--143. Dibble, R.R., 1965. Volcanic seismology. In: B.N. Thompson, L.O. Kermode and A. Ewart (Editors), N e w Zealand Volcanology, Central Volcanic Region. N.Z. Dep. Sci. Ind. Res.,Inf. Ser., 50: 93--98. Dibble, R.R., 1966. Seismic recordings of subterranean volcanic activity at Ruapehu during 1964. Bull. Volcanol., 29: 761--762. Dibble, R.R., 1969. Seismic power recordings during hydrothermal eruptions from Ruapehu Crater Lake in April 1968. J. Geophys. Res., 74: 6545--6551. Dibble, R.R., 1972. Seismic and related phenomena at active volcanoes in N e w Zealand, Hawaii and Italy. Ph.D. Thesis, Victoria University, Wellington (unpublished). Dibble, R.R., 1974. Volcanic seismology and accompanying activity of Ruapehu volcano, N e w Zealand. In: L. Civetta, P. Gasparini, G. Luongo and A. Rapolla (Editors), Physical Volcanology. Elsevier, Amsterdam, pp. 49--85. Friedlander, B., 1898. Some notes on the volcanoes of the Taupo District. Trans. N.Z. Inst., 31: 498--510. Giggenbach, W.F., 1974. The chemistry of Crater Lake, Mt. Ruapehu (New Zealand), during and after the 1971 active period. N.Z.J. Sci., 17: 33--45. Giggenbach, W.F., 1975. Variations in the carbon, sulfur and chlorine contents of volcanic gas discharges from White Island, New Zealand. Bull. Volcanol., 39: 15--27. Giggenbach, W.F. and Glover, R.B., 1975. The use of chemical i n d i c a t o r s ~ surveillance of volcanic activity affecting the Crater Lake on Mt. Ruapehu, New Zealand. Bull. Volcanol., 39: 70--81.

236 Gregg, D.R., 1960. Volcanoes of Tongariro National Park. N.Z. Dep. Sci. Ind. Res., Inf. Ser., 28:123 pp. Hales, A.L., 1937. Convection currents in Geysers. Mon. Not. R. Astron. Soc., Geophys. Suppl., 4: 122--131. Healy, J., 1973a. Volcano surveillance, Tongariro National Park. N.Z. Volcanol. Rec., 1 : 1--9. Healy, J., 1973b. Volcano observations, 1971. Ruapehu. N.Z. Volcanol. Rec., 1 : 10--12. Healy, J., Lloyd, E.F., Rishworth, D.E.H., Wood, C.P., Glover, R.B. and Dibble, R.R., 1978. The eruption of Ruapehu, New Zealand, on 22 June 1969. N.Z. Dep. Sci. Ind. Res., Bull., 224:80 pp. Hurst, A.W., 1980. Temperature observations of Crater Lake, Mt Ruapehu, New Zealand, using temperature telemetry buoys. Bull. Volcanol., 43: 121--129. Irwin, J., 1972. New Zealand lakes bathymetry surveys 1965--1970. N.Z. Oceanogr. Inst., Rec., 1(6): 107--126. Nairn, I.A., 1974. Ruapehu; observations and inspections. N.Z. Volcanol. Rec., 2: 11--15. Nairn, I.A., 1975a. Ruapehu; observations and inspections. N.Z. Volcanol. Rec., 3: 24--28. Nairn, I.A., 1975b. Ruapehu; observations and inspections. N.Z. Volcanol. Rec., 4: 27--30. Nairn, I.A., 1976. Ruapehu; observations and inspections. N.Z. Volcanol. Rec., 5: 23--26. Nairn, I.A., Wood, C.P., Hewson, C.A.Y. and Appendix Otway, P.M., 1979. Phreatic eruptions of Ruapehu April 1975. N.Z.J. Geol. Geophys., 22: Odell, N.E., 1955. Mount Ruapehu, New Zealand. Observations on its crater lake and glaciers. J. Glaciol., 2: 599---605. O'Shea, B.E., 1954. Ruapehu and the Tangiwai disaster. N.Z.J. Sci. Technol., Sect. B, 36: 174--189. Reed, J.J., 1945. Activity at Ruapehu, March-April 1945. N.Z.J. Sci. Technol., B27: 17--23. Rose, J.H., 1954. The Crater Lake, Mount Ruapehu. N.Z. Alpine J., 15: 539. Scott, B.J., 1977. Ruapehu; observations and inspections. N.Z. Volcanol. Rec., 6: 21--23. Scott, B.J., 1978. Ruapehu; observations and inspections. N.Z. Volcanol. Rec., 7: 22--25. Sutton, O.G., 1951. Atmospheric turbulence and diffusion. In: T.F. Malone (Editor), Compendium of Meteorology. American Meteorological Society, Boston, Mass., pp. 492--509. Turner, J.S., 1973. Buoyancy Effects in Fluids. Cambridge University Press, Cambridge, 367 pp. Veronis, G., 1965. On finite amplitude instability in thermohaline convection. J. Mar. Res., 23: 1--17. Weisman, R.N. and Brutsaert, W., 1973. Evaporation and cooling of a lake under unstable atmospheric conditions. Water Resour. Res., 9 : 1242--1257.